Lesson Plan for Numbering, Worksheets, and Exams

Lesson Plan Course Title: Computer Maintenance

Session Title: Numbering Systems

Lesson Duration: Lesson length is subjective and will vary from instructor to instructor Performance Objective: Upon completion of this assignment, the student will be able to identify the places in binary, decimal, and hexadecimal numbers and know the value of each. The student will work with powers of 16 and relate them to hexadecimal places, powers of 10 and relate them to decimal places, as well as powers of 2 and relate them to binary places.

Specific Objectives: · Demonstrate the ability to convert decimal numbers into binary and hexadecimal numbers. · Demonstrate the ability to convert binary numbers into decimal and hexadecimal numbers. · Demonstrate the ability to convert hexadecimal numbers into decimal and binary numbers.

Preparation

TEKS Correlations: §130.273. Computer Maintenance (4) The student acquires an understanding of computer technologies. The student is expected to: (F) explain the relationships relative to data-communications theory

Instructor/Trainer References: 1. Cisco Systems Networking Academy Program: IT Essentials I: PC Hardware and Software, Chapter 1: Information Technology Basics. 2. Cisco Systems Networking Academy Program: CCNA Semester 1, Chapter 1: Computing Basics, and Chapter 6: Layer 2 Concepts. 3. JES and Co., A+ Certification: Introduction to Computer Hardware, Lesson 8: System Settings: BIOS, IRQ, I/O, and DMA.

Instructional Aids: 1. PowerPoint Presentation: Numbering Systems 2. PowerPoint Presentation Handouts: Numbering Systems 3. Worksheet exercise: Binary numbers (and key) 4. Worksheet exercise: Binary to decimal conversion (and key) 5. Worksheet exercise: Decimal to binary conversion (and key) 6. Worksheet exercise: Hexadecimal conversion (and key) 7. Numbering Systems Exam (and key)

Materials Needed: 1. Copies of Worksheets for each student 2. Copies of Exam for each student

IT: Computer Maintenance: Numbering Systems Plan UNT in partnership with TEA, Copyright © . All rights reserved 1 Equipment Needed: 1. A projection system to display the PowerPoint presentation [PC/Monitor, PC/Projector, etc.]

Learner Students should read the appropriate curriculum material for Numbering Systems [depending on the text/curriculum being used for this course]. This lesson can be taught with only the PowerPoint presentation and worksheet handouts.

Introduction

MI Introduction (LSI Quadrant I): Having sharp skills in number systems will aid you in your career as an IT professional. With the ability to convert numbers without the use of a calculator, you will be able to quickly and easily solve problems that may arise.

Computer systems use the binary numbering system to operate. Why do you think binary is referred to as the “natural” numbering system for computers to accomplish their tasks?

[Computers and networking equipment use binary numbers, a series of BITS (short for binary digits) that are either ON (a binary 1) or OFF (a binary 0). They are encoded internally in the PC on microchips and on the computer motherboard’s bus as electrical voltages]. Understanding binary numbers and how they relate to decimal numbers is critical to understanding how computers work internally.

Outline

MI Outline (LSI Quadrant II): Instructor Notes:

1. Introduce numbering systems to students using a PowerPoint presentation. a. Introduce the students to the base 10 numbering system (decimal). b. Introduce the students to the base 2 numbering system (binary). c. Introduce the students to the base 16 numbering system (hexadecimal). d. Compare and contrast decimal and binary counting. e. Demonstrate decimal to binary conversion [two methods]. f. Demonstrate binary to decimal conversion [two methods]. g. Introduce hexadecimal to decimal conversion. h. Discuss basic hexadecimal numbering. i. Demonstrate hexadecimal to binary conversion. j. Demonstrate decimal to hexadecimal conversion. k. Demonstrate hexadecimal to decimal conversion. l. Demonstrate binary to hexadecimal conversion.

2. Students practice number conversion exercise using

IT: Computer Maintenance: Numbering Systems Plan UNT in partnership with TEA, Copyright © . All rights reserved 2 worksheets. a. Students complete the worksheet exercise for binary numbers. b. Students complete the worksheet exercise for binary to decimal conversion. c. Students complete the worksheet exercise for decimal to binary conversion. d. Students complete the worksheet exercise for hexadecimal conversion.

Application MI Guided Practice (LSI Quadrant III): 1. Teacher works through the first conversion problem on each worksheet prior to assigning the worksheet to the student for individual completion.

2. Have the students work through the second conversion problem on each worksheet with their peers; rework if necessary.

3. Teacher assists student pairs, providing guidance as necessary or has students volunteer to work/explain problem 2 for the class.

MI Independent Practice (LSI Quadrant III): 1. Students work independently to complete number system worksheets: a. Students complete the worksheet exercise for binary numbers b. Students complete the worksheet exercise for binary to decimal conversion c. Students complete the worksheet exercise for decimal to binary conversion d. Students complete the worksheet exercise for hexadecimal conversion

Summary

MI Review (LSI Quadrants I and IV): 1. Ask students summary questions. a. What are the symbols used by base 2? [0, 1] b. What are the symbols used by base 10? [0, 1, 2, 3, 4, 5, 6, 7, 8, 9] c. What are the symbols used by base 16? [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F] d. Can you describe a method of converting a decimal number to binary? e. Can you describe a method of converting a binary number to decimal?

2. Demonstrate [one more time] the conversion procedures the students have just experienced. a. Binary to decimal example b. Decimal to binary example c. Binary to hexadecimal example d. Hexadecimal to binary example

MI Informal Assessment (LSI Quadrant III):

The teacher will monitor student progress during independent practice and provide

independent re-teach/redirection as needed.

MI Formal Assessment (LSI Quadrant III, IV):

Administer the Numbering Systems Exam.

Extension

MI Extension/Enrichment (LSI Quadrant IV):

1. Students that have mastered the conversion techniques can peer-tutor students [one-on-one] that are having difficulty solving the conversions. 2. Students can show their conversion techniques on the board for the entire class to observe. 3. Students can observe their computer’s network interface card (NIC) MAC address in hexadecimal, and convert the MAC address to binary and decimal.

Personal Development Icon MI Teaching Strategies Strategies Lecture, discussion, journal Reading, highlighting, outlining, Verbal/ writing, cooperative learning, teaching others, reciting information Linguistic word origins Problem-solving, number Organizing material logically, explaining Logical/ games, critical thinking, things sequentially, finding patterns, Mathematical classifying and organizing, developing systems, outlining, charting, Socratic questioning graphing, analyzing information Mind-mapping, reflective Developing graphic organizers, mind- time, graphic organizers, mapping, charting, graphing, organizing Visual/Spatial color-coding systems, with color, mental imagery (drawing in drawings, designs, video, the mind’s eye) DVD, charts, maps Use music, compose songs Creating rhythms out of words, creating Musical/ or raps, use musical rhythms with instruments, playing an Rhythmic language or metaphors instrument, putting words to existing songs Use manipulatives, hand Moving while learning, pacing while signals, pantomime, real life reciting, acting out scripts of material, Bodily/ situations, puzzles and board designing games, moving fingers under Kinesthetic games, activities, role- words while reading playing, action problems Reflective teaching, Reflecting on personal meaning of interviews, reflective listening, information, studying in quiet settings, Intrapersonal KWL charts imagining experiments, visualizing information, journaling Cooperative learning, role- Studying in a group, discussing Interpersonal playing, group brainstorming, information, using flash cards with cross-cultural interactions others, teaching others

Natural objects as Connecting with nature, forming study Naturalist manipulatives and as a groups with like-minded people background for learning Socratic questions, real life Considering the personal relationship to situations, global the larger context Existentialist problems/questions

Bin ar y t o Dec im al This binary Equals this number... 11111111decimal number 27 26 25 24 23 22 21 20 12 8 + 64 ++++++32 16 48 2 1 = 2 5 5

This binary Equals this number... 10010101decimal number 27 26 25 24 23 22 21 20 12 8 + ++++++16 4000 0 1 = 14 9

Convert each binary number into a decimal number.

1. 1 1 0 0 1 0 0 1 = 9. 0 1 1 0 1 1 1 0 =

2. 0 1 0 0 0 1 1 1 = 10. 0 0 0 1 0 1 1 1 =

3. 1 0 0 0 0 1 1 0 = 11. 1 1 1 1 1 0 0 0 =

4. 0 0 0 1 0 0 0 1 = 12. 1 1 1 0 0 0 1 0 =

5. 1 0 0 0 1 0 0 0 = 13. 0 0 0 1 1 1 0 1 =

6. 0 0 1 1 1 1 1 0 = 14. 0 1 1 0 1 1 1 1 =

7. 0 1 0 1 0 1 0 1 = 15. 1 0 0 1 0 1 1 1 =

8. 1 0 1 0 1 0 1 0 = 16. 1 1 1 0 0 1 0 1 =

1 1 0 0 1 0 0 1 201 0 1 1 0 1 1 1 0 110 0 1 0 0 0 1 1 1 71 0 0 0 1 0 1 1 1 23 1 0 0 0 0 1 1 0 134 1 1 1 1 1 0 0 0 248 0 0 0 1 0 0 0 1 17 1 1 1 0 0 0 1 0 226 1 0 0 0 1 0 0 0 136 0 0 0 1 1 1 0 1 29 0 0 1 1 1 1 1 0 62 0 1 1 0 1 1 1 1 111 0 1 0 1 0 1 0 1 85 1 0 0 1 0 1 1 1 151 1 0 1 0 1 0 1 0 170 1 1 1 0 0 1 0 1 229

Decimal to Binary 15 1 This decimal Equals this 128? YE S 151 number... = binary number 12 8 1286432168 42 1 23 64? NO 32? NO 1 0 0 1 0 1 1 1 16? YE S 16 27 26 25 24 23 22 21 20 7 8? N O 4 4? YES 3 2 2? YES 1

1 1? YE S 0

Convert each decimal number into a binary number.

1. 137 = 11. 200=

2. 12 8 = 12. 171=

3. 63= 13. 15 0 =

4. 213= 14. 27=

5. 49= 15. 19 =

6. 111= 16. 189 =

7. 242= 17. 222=

8. 19 2 = 18. 79 =

9. 89 = 19. 73=

10. 2= 20. 136 =

137 1 0 0 0 1 0 0 1 200 1 1 0 0 1 0 0 0 128 1 0 0 0 0 0 0 0 171 1 0 1 0 1 0 1 1 63 0 0 1 1 1 1 1 1 150 1 0 0 1 0 1 1 0 213 1 1 0 1 0 1 0 1 27 0 0 0 1 1 0 1 1 49 0 0 1 1 0 0 0 1 19 0 0 0 1 0 0 1 1 111 0 1 1 0 1 1 1 1 189 1 0 1 1 1 1 0 1 242 1 1 1 1 0 0 1 0 222 1 1 0 1 1 1 1 0 192 1 1 0 0 0 0 0 0 79 0 1 0 0 1 1 1 1 89 0 1 0 1 1 0 0 1 73 0 1 0 0 1 0 0 1 2 0 0 0 0 0 0 1 0 136 1 0 0 0 1 0 0 0

Student Name: Date:

HEXADECIMAL CONVERSIONS

INSTRUCTIONS: Convert the following numbers to their appropriate base forms. Record your answers in the spaces provided in the table.

BASE 10 BASE 2 BASE 16 243 10101100 AE 110110 131 3F 98 10010001 146 11000011 4D 11110001 172 E2 100100 195 31 1001111 7B 146 5A 11100000 223

INSTRUCTIONS: Convert the following numbers to their appropriate base forms

BASE 10 BASE 2 BASE 16 243 11110011 F3 172 10101100 AC 174 10101110 AE 54 110110 36 131 10000011 83 63 111111 3F 98 11000010 62 145 10010001 91 146 10010010 92 195 11000011 C3 77 1001101 4D 241 11110001 F1 172 10101100 AC 226 11100010 E2 36 100100 24 195 11000011 C3 49 110001 31 79 1001111 4F 123 1111010 7B 146 10010010 92 90 1011010 5A 224 11100000 E0 223 11011111 DF

Introduction to Binary Numbers

Part 1 Decimal Binary Part 2 Fill in the rest of N ow write the the numbers, in 0 binary number order. 1 for each decimal number

Part 3 Fill in the decimal and binary equivalents of each exponent.

Decimal Binary 20= 21= 22= 23= 24 = 25= 26= 27=

32 64 12 8

Part 1 Part 2 Part 3 Decimal Binary Decimal Binary

0 0 20 1 1 1 1 21 2 10 2 10 21 4 100 3 11 23 8 1000 4 100 24 16 10000 5 101 25 32 100000 6 110 26 64 1000000 7 111 27 128 10000000 8 1000 9 1001 10 1010 11 1011 12 1100 13 1101 14 1110 15 1111 16 10000 32 100000 64 1000000 128 10000000

Student Name:

Date:

NUMBERING SYSTEMS EXAM

DIRECTIONS: Circle the letter that corresponds to the one (1) best answer for each of the questions below.

Question 1: All functions of a computer are based upon the use and manipulation of numbers. Which number system is most native to a computer?

A. binary B. decimal C. hexadecimal D. octal

Question 2: What is the decimal conversion of the binary number 11011001?

A. 221 B. 193 C. 217 D. 192

Question 3: What is the hexadecimal conversion of the decimal number 224?

A. F0 B. E0 C. 92 D. 9E

Question 4: What is the decimal conversion of the hexadecimal number 7F?

A. 115 B. 134 C. 201 D. 127

Question 5: What is the binary conversion of the hexadecimal number CB?

A. 10111001 B. 11100001 C. 11000100 D. 11001011

Question 6: Which binary number represents the decimal number 133?

A. 10001011 B. 11000001 C. 10000111 D. 10000101

Question 7: What is the hexadecimal equivalent of the decimal number 241?

A. E7 B. D3 C. F1 D. A9

Question 8: What is the decimal value of the binary number 11111111?

A. 0 B. 64 C. 192 D. 255

Question 9: What is the definition of a bit?

A. the section of a network that is bounded by bridges, routers, or switches B. a binary digit used in the binary number system, either 0 or 1 C. the interface on an internetworking device, such as a router D. the network areas within which data packets that have collided are propagated

Question 10: Which of the following phrases best describes the decimal numbering system?

A. It is also called the Base 100 Number System. B. It is based on powers of 1. C. It uses the 10 symbols 0 - 9. D. It is the same as the ASCII numbering system.

Question 11: Which numbering system is based on powers of 2?

A. octal B. hexadecimal C. binary D. ASCII

Question 12: What is the decimal number 151 in binary?

A. 10010111 B. 10010110 C. 10101011 D. 10010011

Question 13: What is the binary number 11011010 in decimal?

A. 218 B. 202 C. 222 D. 186

Question 14: Convert the decimal number 43 to Hex.

A. 2B B. 1F C. EF D. 1A

Question 15: Hexadecimal is used to represent what kind of addresses?

A. IP B. Octal C. MAC D. Digital

Question 16: What is 16 raised to the first power (16 1 )?

A. decimal 1 B. decimal 16 C. hex FF D. hex 16

Question 17: Convert the decimal number 2989 to Hex.

A. FDD1 B. BAD C. ED D. CAD

Question 18: What is the decimal value of the hex number ABE?

A. 2750 B. 5027 C. 2570 D. 7250

Question 19: What is the hex value of the binary number 11100010?

A. D2 B. E2 C. G2 D. H20

Question 20: Which numbering system is based on powers of 10?

A. octal B. hexadecimal C. binary D. decimal

Numbering Systems Exam Key